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Our big question is; is all of this based on hindsight? How can you convince us this is forward-looking? I need to understand the why.

Keep in mind that when we build a strategy around covariance we’re not making a prediction of which way a stock is going to move, we’re focusing on the relationship between the stocks. The reason historic covariance is predictive is because it very reliably identifies structural relationships between stocks.

A good example is the relationship between oil and airlines. When oil drops in price, airlines go up because their number one operating cost went down. In general, whenever there’s a strong correlation or anti correlation between assets, it is due to a fundamental relationship like that.

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We don’t believe you can forecast a future price with any consistency.

Indeed, our forecasting very noisy. Any Machine Learning or AI-based system will be. We’d like to emphasize that we’re against fully automated trading. All of our successful strategies include a human element. The best approach is to combine the best capabilities of machine and human. Namely: Leverage the machine to evaluate all the thousands of stocks in the market continuously, and have it provide a manageable number of opportunities. Then apply the human intellect for final selection.

For the most part we agree with those articles. MPT as a whole has not worked in the recent decade, but there are pieces of MPT that remain valuable. Our approach is to leverage the parts that work and deemphasize or replace the problematic aspects.

There are three key inputs to a Mean Variance Optimizer (MVO): 1) An alpha vector, or forecast for each equity, 2) Historical covariance between each equity and every other one, 3) Historical volatility for each equity. In order for optimization to work over time, the values for each of these factors must reasonably predict their future values.

Of these three inputs, price prediction is the achilles heel. In traditional MVO recent returns are used for the future forecast. As it turns out recent returns are really poor predictors. And even good forecasters like ours are subject to significant noise. On the other hand, historic covariance and volatility are excellent predictors of future covariance and volatility. Our recommendation is to emphasize the use of these most predictive factors and to downplay the use of price prediction.

Our research shows that we can improve almost any portfolio or strategy in this way.

Doesn’t this mean that using the Price Forecaster as the basis for the Optimization method is thus not recommended by you?

The optimizer requires some alpha input. Recent returns (the traditional input) is a terrible alpha predictor. Even though it is admittedly noisy, our Price Forecaster is a better choice. It’s even better to use an input that combines human insight informed by our tools.

What does all of this mean for the Forecasting module and how it should best be utilized by a Portfolio Manager to extract something consistently predictive?

I recommend a two step process: 1) The PM should pre-screen stocks to build a “shopping list” using their proprietary insight; 2) Leverage the Price Forecaster to prioritize this list for addition to a portfolio. Depending on the PM’s preferences, it could also make sense to reverse these steps by using the forecaster first to build a short list that is then prioritized by the PM.

Factor models are different for each stock, not all the same. Your correlations will last or your correlations will break – you don’t know. It’s the most difficult area.

If the underlying factors between stocks are significantly different, the correlation will be poor (likely close to 0). On the other hand factor models change slowly because they reflect the underlying structure of the company’s business. So we see that correlations change slowly as well.